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An interface anticrack in a periodic two-layer piezoelectric space under vertically uniform heat flow

Kaczyński A., Kaczyński B.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 3

667--681

This paper aims to investigate 3D static thermoelectroelastic problem of a uniform heat flow in a bi-material periodically layered space disturbed by a thermally and electrically-insulated rigid sheet-like inclusion (so-called anticrack) situated at one of the interfaces. An approximate analysis of the considered laminated composite is given in the framework of the homogenized model with microlocal parameters. Accurate results are obtained by constructing suitable potential solutions and reducing to the corresponding homogeneous thermoelectromechanical (or thermomechanical) anticrack problems. The governing boundary integral equation for a planar interface anticrack of arbitrary shape is derived in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and interpreter from the failure perspective. Unlike existing solutions for defects at the interface of materials, the solution obtained displays no oscillatory behavior.

On 3D symmetrical thermoelastic anticrack problems

Kaczyński A.

Archives of Mechanics

2016

Vol. 68, nr 2

99--112

A potential theory method is developed to solve a symmetrical thermoelastic problem of a cooling temperature field applied over the faces of a rigid sheet-like inclusion (an anticrack) in an elastic space. The governing boundary two-dimensional (2D) singular integral equations for an arbitrarily shaped anticrack are derived in terms of unknown thermal shear stress jumps. As an illustration, a complete solution expressed in elementary functions to the problem of a circular rigid inclusion subjected to a uniform temperature is presented and interpreted from the point of view of fracture theory.

On the thermoelastic problem of uniform heat flow disturbed by a circular rigid lamellate inclusion

Kaczyński A., Monastyrskyy B.

Archives of Mechanics

2009

Vol. 61, nr 3-4

309-324

A complete solution in elementary functions is given for the three-dimensional thermoelastic ?eld in an elastic space, containing an absolutely rigid circular inclusion (anticrack) under a normally incident uniform heat ?ow. The inclusion is assumed to be slightly conducting, with a certain thermal resistance. The analysis is based on the potential theory method. The resulting boundary-value problems are reduced to classical mixed problems of the potential theory. The temperature, ?uxes, thermal stresses and displacements in the inclusion plane are given in closed forms and interpreted from the point of view of the failure theory.